17-Swaps and Credit Derivatives

1. 17-Swaps and Credit Derivatives

2. Questions • What is an interest rate swap? • How is it used to hedge interest rate risk? • How does comparative advantage create swap opportunities? • What is a credit default swap? • What is the no arbitrage CDS rate?

3. Swaps • An agreement between two parties to exchange cash flows in the future. • Cash flows and dates when cash is exchanged are specifically defined. • Example: • A agrees to pay B the Libor rate at the end of each • “B” agrees to give “A” 9.95% • Both rates are a percentage of some notional amount Libor A B 9.95% (fixed)

4. Swaps: What is the Purpose? • Example: • Banks have a natural mismatch between the durations of assets and liabilities. • As a result, equity takes a hit when rates go up.

5. Example:Asset & Liability Management • Risk Management Techniques • Reduce the duration of the assets. • Increase the duration of the liabilities. • Take a short position on treasury futures • Buy a put on treasury bonds or treasury futures. • Use an interest rate swap.

6. Interest Rate Swaps • Example: An interest rate swap • principal value of $1M • exchanges annually • Floating cash flow: one-year LIBOR rate plus 5.5% • Fixed cash flow: 9.5% interest rate • Maturity: thirty years. • The Bank may want to pay fixed and receive floating

7. Cash Flows of Floating for Fixed Swap • The swap does not cost anything upfront. • This swap is equivalent to going long in floating-rate bonds (lending money at a floating rate) and going short in fixed-rate bonds (borrowing money at a fixed rate).

8. Swaps and Comparative Advantage • A bank has a small client called “the firm” • Suppose the banks and the firm can borrow at rates: FixedFloating Bank 10% Libor+0.3% Firm 12% Libor+1.0% • Who has the better credit rating?

9. Swaps and Comparative Advantage • Note that the firm pays 2% more in fixed markets and only .7% more in floating markets. • If the default risk of the firm increases: • Floating rate lenders can charge higher rates, or refuse to roll-over loans • Fixed-rate lenders are stuck and will likely be stuck with losses

10. Swaps and Comparative Advantage • Relative to the bank, the firm has a comparative advantage in floating markets • Relative to the firm, the bankhas a comparative advantage in fixed markets.

11. Swaps and Comparative Advantage • Suppose the bank has more tolerance for bearing the default risk of the firm than the market • Since the firm is a client of the bank, the bank has “insider information” about the financial health of the firm • Suppose the firm wants to borrow at fixed • wants to avoid interest rate risk • Can the two enter a swap and be better off than borrowing at market rates?

12. Swaps and Comparative Advantage • Suppose the firm borrows from outside lenders at L+1% • Suppose the bank borrows from outside lenders at 10% • The bank and the firm can then enter a swap with • The firm paying the bank a fixed rate 11.35 • The bank paying the firm a floating rate L + 1%

13. Swaps and Comparative Advantage • The firm • Pays Libor +1% (outside lenders) • Receives Libor + 1% (from the bank) • Pays 11.35% (to the bank) • Net: Paying 11.35% Fixed • (.65% better than at fixed market rates) • The bank • Pays 10% (outside lenders) • Receives 11.35% (from the firm) • Pays Libor + 1 % • Net: Paying Libor – 0.35% • (.65% better than at floating market rates)

14. Swaps and Comparative Advantage • Cost to bank: bears default risk of firm • May be willing to do so if it wants to maintain the firm as a client and is generating fees from other services it is offering the client. • Bank has insider information • Firm pays 11.35% fixed only if it can continue to borrow floating at 1% over Libor. • If default risk increases, firm could lose benefit of swap.

15. Swaps and Comparative Advantage One simple approach: • Each firm borrows in market (fixed or floating) in which it has a comparative advantage. • Swap Rates: • Floating rate is same as floating rate of company borrowing at floating rate. • Fixed Rate is same as fixed rate of company borrowing at floating rate less X%

16. Swaps and Comparative Advantage • How to find X • Find total possible gain • Difference in fixed rates minus difference in floating rates • Divide this difference by 2 • Setting up the swap in this way will allow the bank and firm to split the gain.

17. Credit Derivatives • Credit derivatives are financial contracts designed to reduce or eliminate credit risk exposure by providing insurance against losses suffered due to credit events. • Banks can repackage and parcel out credit risk while retaining assets on balance sheet and thus maintain client relationships. • Bank can transfer the credit risk of illiquid assets if it cannot transfer the assets themselves.

18. Credit Default Swap (Bank) (Speculator in credit derivatives)

19. Basic Contract terms • Reference Entity • The underlying asset (e.g., a bond) • Notional Amount • Value of reference entity at swap origination • Maturity • Date when swap contract matures • Credit events • Bankruptcy, failure to pay, debt restructuring • Price • Fixed-rate to be paid/received

20. Example • Reference Entity • $10 million dollar bond • Notional Amount • $10 million (par value) • Maturity • 5 years • Credit events • Bankruptcy, failure to pay, debt restructuring • If a credit event occurs, protection seller pays par value of bond • Note that protection seller bears interest-rate risk • Price • 500 basis points

21. Example: $10M 5 year CDS @ 500 basis points with No Credit Event

22. Example: $10M 5 year CDS @ 500 basis points with Credit Event and accrued interest Contract is terminated. No further payments.

23. Growth of Underlying CDS Market Trillions Source: “Bear Sterns Structured Credit Products”, December 2005

24. Credit Default Swap - Pricing • Swap Rate = Default risk premium • Short Swap: Sell protection in the default swap market and earn the swap rate • or • Borrow at risk-free, buy bond, and earn the spread

25. Example • Zero coupon bond • Matures in one year • Face value: 1000 • Probability of default: 25% • Recovery rate: 60% • Price: 841.12 • Risk-free rate: 5% • Swap rate: YTM – 5% = 18.89% - 5% = 13.89%

26. Example • Borrow 841.12, buy bond • Cost: 0 • No default payoff: 1000 – 841.12*(1.05) = 116.82 • Default payoff: 600 - 841.12*(1.05) = -283.18 • Go short a swap on bond • Cost: 0 • No default payoff: .1389*841.12 = 116.83 • Default payoff: 600 – 1000 + .1389*841.12 = -283.18

27. Example • If swap rate is not 13.89%, then an arbitrage opportunity exists. • Suppose swap rate is 15% • Go short swap • Short bond (assuming its possible) • Invest proceeds at risk-free rate

28. Example • No default: • Short swap: get .15*841.12 = 126.17 • Risk-free account: get 1.05*841.12=883.18 • Short bond: must pay out 1000 • Total: 126.17+883.18-1000 = 9.35 • Default: • Short swap: get .15*841.12 =126.17 • Short swap: pay out 1000 • Short swap: get bond (use to close out short position) • Risk-free account: get 1.05*841.12=883.18 • Total: 126.17-1000+883.18= 9.35

29. Example • In either state earn 9.35 • Note: 9.35 = [(actual swap rate) – (no-arbitrage swap rate)]*P =(.15 - .1389)*841.12 • If actual swap rate < no-arbitrage swap rate • Go long swap • Borrow money, buy bond

30. Example • Actual swap rate = 12% • No default: • long swap: pay out .12*841.12 = 100.94 • Liability: pay out 1.05*841.12=883.18 • Long bond: get 1000 • Total: 1000-883.18-100.94= 15.88 • Default: • long swap: pay out .12*841.12 = 100.94 • Liability: pay out 1.05*841.12=883.18 • Long swap: get 1000 • Total: 1000-883.18-100.94 =15.88